Use synthetic division to find the quotient and remainder when the first polynomial is divided by the second. Then,use the remainder theorem to verify your answer. Work for both of these operations must be shownProblem attached as well **Instructions for Polynomial Division:**Use synthetic division to find the quotient and remainder when the first polynomial is divided by the second. Then, use the remainder theorem to verify your answer. Work for both of these operations must be shown!Given Polynomials:1. \(2x^4 - x^3 - 15x^2 + 3x + 3, x + 3\)**Steps to Follow:**1. **Set up the synthetic division**: For synthetic division, rewrite the division problem in the form where \((x + 3)\) is factoring out \(-3\). Polynomial to divide: \(2x^4 - x^3 - 15x^2 + 3x + 3\)2. **Perform Synthetic Division**: - Write the coefficients of the polynomial: \(2, -1, -15, 3, 3\). - Use the zero of the divisor, which is -3 (since we are dividing by \(x + 3\), we use \(-3\) for synthetic division). Use the procedure of synthetic division to determine the quotient and the remainder.3. **Remainder Theorem**: - Verify your answer using the remainder theorem, which states that the remainder of the division of a polynomial \(f(x)\) by a binomial \(x - c\) is \(f(c)\).**Expected Results:**- After completing synthetic division, you should find the quotient polynomial.- The remainder should be a constant, confirming the results from the synthetic division.- Use the remainder theorem to verify that plugging \(-3\) into the original polynomial results in the same remainder.Ensure all steps are documented clearly, with all intermediate steps shown for full comprehension.

Answered: Image /qna-images/answer/14c1286f-b6b9-4ce6-8ebc-99e43548aada.jpg

Use synthetic division to find the quotient and remainder when the first polynomial is divided by the second. Then, use the remainder theorem to verify your answer. Work for both of these operations must be shown! 1) 2x4-x3- 15x2 + 3x, x + 3

Use synthetic division to find the quotient and remainder when the first polynomial is divided by the second. Then, use the remainder theorem to verify your answer. Work for both of these operations must be shown! 1) 2x4-x3- 15x2 + 3x, x + 3

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: +2x-2 h(x) 5x +

Q: How do I use synthetic division to find the quotient and the remainder of a problem that has…

A: Let us have to divide (2x3-4x2+x-5) by (x-2) using synthetic division. Then we will consider the…

Q: Create a cubic expression that when divided by (x-1) will have a remainder of 6

Q: Use synthetic division to divide. (x2 - 9x +20) + (x- 4)

A: Steps to perform while doing synthetic division: 1) To write the given problem in a division like…

Q: Divide the following using long division. Specify if the divisor is a factor or not. 12-3x +2x 7) 8)…

Q: CX+3x-5) 小(メナ)

Q: I'm really confused with this type of question. Help please

A: The given polynomial, P and a constant value, c is,

Q: The product of two rational expressions is the product of their divided by the product of their.

A: The rational expressions are of the form pq where p and q are polynomials , such that q≠0. The…

Q: When doing calculus problems, how would I identify that I should do long division of polynomials in…

A: 1. Polynomial division: If you're asked to divide one polynomial by another, long division is…

Q: if the equation is x^3-5x^2+4x-20 and I've been given the zero: -2i couldn't I just factor the…

Q: nomial in factored form and then in

A: Here we have to create a polynomial of, a) Degree 4 b) One fractional zero with a multiplicity of…

Q: Here is an example of the question. I need to find the polynomial expression that represents the…

A: To Determine: find the total surface area of the table in the figure Given: we have a figure in…

Q: 12.-/1 pointsLarPreCalcRMRP72.3.028.MI. Use synthetic division to divide. (6x + 3x + 8) + (x+2) to

Question

Use synthetic division to find the quotient and remainder when the first polynomial is divided by the second. Then,use the remainder theorem to verify your answer. Work for both of these operations must be shown

Problem attached as well

**Instructions for Polynomial Division:**

Use synthetic division to find the quotient and remainder when the first polynomial is divided by the second. Then, use the remainder theorem to verify your answer. Work for both of these operations must be shown!

Given Polynomials:
1. \(2x^4 - x^3 - 15x^2 + 3x + 3, x + 3\)

**Steps to Follow:**

1. **Set up the synthetic division**: For synthetic division, rewrite the division problem in the form where \((x + 3)\) is factoring out \(-3\).

Polynomial to divide: \(2x^4 - x^3 - 15x^2 + 3x + 3\)

2. **Perform Synthetic Division**:
- Write the coefficients of the polynomial: \(2, -1, -15, 3, 3\).
- Use the zero of the divisor, which is -3 (since we are dividing by \(x + 3\), we use \(-3\) for synthetic division).

Use the procedure of synthetic division to determine the quotient and the remainder.

3. **Remainder Theorem**:
- Verify your answer using the remainder theorem, which states that the remainder of the division of a polynomial \(f(x)\) by a binomial \(x - c\) is \(f(c)\).

**Expected Results:**
- After completing synthetic division, you should find the quotient polynomial.
- The remainder should be a constant, confirming the results from the synthetic division.
- Use the remainder theorem to verify that plugging \(-3\) into the original polynomial results in the same remainder.

Ensure all steps are documented clearly, with all intermediate steps shown for full comprehension.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Use synthetic division to find the quotient and remainder when 3 x'+5x-3x+9 is divided by x-5 Quotient: Remainder:
Put it in standard form, divide the following polynomial using long division, and prove your sender by the remainder theorem.
In my precalculus class we are learning how to do long and synthetic division of polynomials by hand. I am struggling with a particular problem because I cannot find an example that divides a polynomial by something more complex than x+a. I'm working with: (6x^4 -3x^3 +29x^2) ÷ (3x^2 +13) If you could give me an example of this solved by hand that I could use for reference for solving other similar problems I would be very appreciative.
How can i use synthetic division to find the zeros of a 4th degree polynomial?